The PD estimate on the entire hyperparameter space \(\Lambda \)  is computed by sampling the Monte Carlo estimate \((\lambda _C^{(i)})_{i \in \mathcal {N}} \sim {P}(\lambda _C)\) , \(\mathcal {N} := \lbrace 1, 2, ..., n\rbrace \) .
We now introduce the PD estimate on a sub-region \(\Lambda ^\prime \subset \Lambda \)  simply as \((\lambda _C^{(i)})_{i \in \mathcal {N^\prime }}\)  only using \(\mathcal {N}^\prime = \lbrace i \in \mathcal {N}\rbrace _{\lambda ^{(i)} \in \Lambda ^\prime }\) . Since we are interested in the marginal effect of the hyperparameter(s) \(S\)  at each \(\lambda _S \in \Lambda _S\) , we will usually visualize the PD for the whole range \(\Lambda _S\) . Thus, all obtained sub-regions should be of the form \(\Lambda ^\prime = \Lambda _S \times \Lambda _C^\prime \)  with \(\Lambda _C^\prime \subset \Lambda _C.\) 
This corresponds to an average of ICE curves in the set \(i \in \mathcal {N}^\prime \) .
The pseudo-code to partition a hyperparameter (sub-)space \(\Lambda \)  and corresponding sample
\((\lambda _C^{(i)})_{i \in \mathcal {N}} \in \Lambda _C\) , \(\mathcal {N} \subseteq \lbrace 1, ..., n\rbrace \) ,
into two child regions is shown in Algorithm REF .
This splitting is recursively applied in a CARTClassification and regression trees-like procedure [1]} to expand a full tree structure, with the usual stopping criteria
(e.g., a maximum number of splits, a minimum size of a region, or a minimum improvement in each node).
In each leaf node, the sub-regional PDP and its corresponding uncertainty estimate are computed by aggregating over all contained ICE curves.
